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I/O Circuits and Models 443 1 I/O Design Considerations, 444
Modeling and Budgeting of Timing Jitter and Noise 549 1 Eye Diagram, 550
System Analysis Using Response Surface Modeling 605 1 Model Design Considerations, 606
PREFACE
Yun Ling of Intel Corporation, who patiently reviewed our math and politely corrected our mistakes. Kevin Slattery of Intel Corporation, for reviewing Chapter 2 and strongly encouraging us to write the book. Paul Hamiltonof Tyco, for reviewing Chapter 6. Gerardo Romo of Intel Corporation, for reviewing Chapters 4 and 12.
INTRODUCTION: THE IMPORTANCE OF SIGNAL INTEGRITY
- COMPUTING POWER: PAST AND FUTURE
- THE PROBLEM
- THE BASICS
- A NEW REALM OF BUS DESIGN
- SCOPE OF THE BOOK
- SUMMARY
Observation of the data suggests that the historical trend shows no sign of slowing down. This means that the rise or fall time of the digital signal must be as fast as possible.
![Figure 1-1 Historical computational power and extrapolation into the future. (Adapted from Moravec [1998].)](https://thumb-ap.123doks.com/thumbv2/123dok/11590910.0/18.892.197.690.227.571/figure-historical-computational-power-extrapolation-future-adapted-moravec.webp)
ELECTROMAGNETIC
FUNDAMENTALS FOR SIGNAL INTEGRITY
MAXWELL’S EQUATIONS
Since a comprehensive study of Maxwell's equations is beyond our scope in this text, we present only the necessary information that relates directly to the specific problems addressed here. Although this brief overview of Maxwell's equations may seem daunting at first, the book will simplify the theory and apply it directly to solving practical real-world problems, allowing readers to extract important concepts from the fog of mathematical calculations so that an intuitive understanding can be imparted. .
COMMON VECTOR OPERATORS
- Vector
- Dot Product
- Cross Product
- Vector and Scalar Fields
- Flux
- Gradient
- Divergence
- Curl
Therefore, the current density function flux is the current flowing through the area and is calculated as. SOLUTION We assume that the current density is constant across the cross-section so that J= azJ =Jzand Is the cross-sectional area of the wire.
WAVE PROPAGATION
- Wave Equation
- Relation Between E and H and the Transverse Electromagnetic Mode The wave equations (2-27) and (2-28) are presented in their most general form,
- Time-Harmonic Fields
- Propagation of Time-Harmonic Plane Waves
The speed of light determines the phase shift of the wave, and the intrinsic impedance describes the relationship between the electric and magnetic fields. For example, a propagating total wave may have part of the electric field propagating in the +z-direction and another in the -z-direction.
ELECTROSTATICS
- Electrostatic Scalar Potential in Terms of an Electric Field
- Energy in an Electric Field
- Capacitance
- Energy Stored in a Capacitor
Since a fundamental unit of an electric field is Newton per Coulomb (described above), the force field in (2-56) can be rewritten in terms of the electric field as. When the weights are pressed together, the energy is stored in the tensioned state of the spring.
MAGNETOSTATICS
- Magnetic Vector Potential
- Inductance
- Energy in a Magnetic Field
The magnitude of the force is F =qvBsinθ, whereθ is the angle between the velocity vector and the magnetic field. Remember that the force is perpendicular to the direction of the current flow, and the current flow is defined by the movement of charge.
POWER FLOW AND THE POYNTING VECTOR
- Time-Averaged Values
To quantify (2-109) in terms of the electric and magnetic fields, we start with the volume energy densities for an electric and a magnetic field, which were derived earlier and are listed here for convenience. When considering the electromagnetic power supplied by a sinusoidal time-varying field, practical measurement considerations tend to favor the time-averaged value of the power rather than the instantaneous value described in (2-115). This is because the time-averaged power entering a passive network, as measured with a wattmeter, is a measure of the power dissipated by heat in all resistive circuit elements.
It is sometimes useful to represent the magnitude of the Poynting vector in terms of the electric or magnetic fields and intrinsic impedance defined in equation (2-53).
REFLECTIONS OF ELECTROMAGNETIC WAVES
- Plane Wave Incident on a Perfect Conductor
- Plane Wave Incident on a Lossless Dielectric
If we apply the boundary conditions for the incident and reflected parts of the electric field, we get which creates the ratio of the incident to the reflected electric field for the electromagnetic wave impinging on the PEC:. In our particular scenario, the plane wave propagates in the TEM mode in the z-direction, so that both the electric and magnetic fields are directed parallel (i.e., tangent) to the dielectric interface boundary. The reflection coefficient is a measure of how much of the wave is reflected back from the intersection between the two media, while the transmission coefficient tells how much of the wave is transmitted.
2-9 If a plane wave propagates in the z direction in free space and collides with a plane dielectric medium whereεr =9.6, how much of the wave propagates.
IDEAL TRANSMISSION-LINE FUNDAMENTALS
TRANSMISSION-LINE STRUCTURES
One of the most common transmission lines is coaxial cable, which is used with cable television. When designing a high-speed digital system, transmission lines are usually manufactured on a printed circuit board (PCB) or a multi-chip module (MCM), which usually consists of conductive traces buried or attached to a dielectric with one or more references. power and ground aircraft. The two most common types of transmission lines used in digital designs are microstrip and tape.
The accompanying cross-section is taken at the given mark so that the position of the transmission lines relative to the ground and power planes can be seen.
WAVE PROPAGATION ON LOSS-FREE TRANSMISSION LINES Transmission lines are designed to guide electromagnetic waves from one point
- Electric and Magnetic Fields on a Transmission Line
- Telegrapher’s Equations
- Equivalent Circuit for the Loss-Free Case
Signal (microstrip) Ground/power Signal (stripline) Signal (stripline) Ground/power Signal (microstrip) Transmission line cross section. Control of the conductor and dielectric layers (referred to as the stackup) is required to make the electrical characteristics of the transmission line predictable. Equations (3-12) and (3-18) are the lossless forms of the telegraph equations, which describe the electrical properties of a transmission line.
Consequently, it is necessary to derive a model for the transmission line in terms of the equivalent inductance L and the capacitance C per unit length.
TRANSMISSION-LINE PROPERTIES
- Transmission-Line Phase Velocity
- Transmission-Line Characteristic Impedance
- Effective Dielectric Permittivity
- Simple Formulas for Calculating the Characteristic Impedance For maximum accuracy it is necessary to use one of the many commercially avail-
- Validity of the TEM Approximation
When the electric field is completely contained within the board, as in the case of a strip line as shown in Figure 3-11b, the effective dielectric constant will equal the dielectric permittivity of the insulating material and signals will propagate more slowly than microstrip traces. When signals are directed to the outer layers of the board, as in the case. Note that effin this set of equations accounts for the finite thickness of the signal conductor when calculating the effective dielectric constant for the microstrip.
Consequently, the electric field develops a component in the direction that contradicts the assumption of the TEM approach.
TRANSMISSION-LINE PARAMETERS FOR THE LOSS-FREE CASE Earlier, we discussed how an electromagnetic wave propagates on a transmis-
- Laplace and Poisson Equations
- Transmission-Line Parameters for a Coaxial Line
- Transmission-Line Parameters for a Microstrip
- Charge Distribution near a Conductor Edge
- Charge Distribution and Transmission-Line Parameters
- Field Mapping
If the total charge is to remain the same as in (3-72), and the transmission line width is normalized to = 1, the charge distribution must satisfy. Example 3-2 Use field mapping techniques to calculate the impedance of a coaxial transmission line, shown in Figure 3-25, where b/a=2 and the permittivity of the dielectric is εr =2.3. Example 3-3 Use field mapping techniques to calculate the impedance and effective dielectric permittivity of the microstrip transmission line shown in Figure 3-26, where w/h=1 and the permittivity of the dielectric material is εr =4.0.
Note that some cells were partitioned between air and dielectric material.
TRANSMISSION-LINE REFLECTIONS
- Transmission-Line Reflection and Transmission Coefficient
- Launching an Initial Wave
- Multiple Reflections
- Lattice Diagrams and Over- or Underdriven Transmission Lines A lattice diagram (sometimes called a bounce diagram) is a graphical technique
- Lattice Diagrams for Nonideal Topologies
- Effect of Rise and Fall Times on Reflections
- Reflections from Reactive Loads
As described above, when a signal is reflected from an impedance discontinuity at the end of the line, a portion of the signal will be reflected back to the source. The left and right vertical lines represent the source end (z=0) and load end (z=l) of the transmission line. In this example, the impedance of the base (Z01) is equal to the impedance of the two legs (Z02), and the legs are the same length (l2=l3).
Note that the complicated interactions between the reflections from each leg seriously compromise the integrity of the signal.
TIME-DOMAIN REFLECTOMETRY
- Measuring the Characteristic Impedance and Delay of a Transmission Line
- Understanding the TDR Profile
Consequently, the duration of the reflection will correspond to twice the delay of the transmission line under test, as shown in Figure 3-43. Assuming the input step has a sufficiently fast rise time, the value of the inductor can be estimated by measuring the area under the inductive peak, as shown in Figure 3-45. Example 3-8 Calculate the shunt capacitance value for the waveform in Figure 3-47, given the circuit shown in Figure 3-46.
3-4 Beginning with Laplace's equation, derive a formula for the characteristic impedance of the stripline shown in Figure 3-51.
CROSSTALK
MUTUAL INDUCTANCE AND CAPACITANCE
- Mutual Inductance
- Mutual Capacitance
- Field Solvers
The mutual inductances are represented by Lij, where andj correspond to the lines associated with the mutual inductance. Examination of equation (4-12) reveals that the effective capacitance of line 1 when it is driven in isolation is equal to the sum of the capacitance to ground and the mutual capacitance between lines 1 and 2. Therefore, the sum of the capacitance to ground plus the mutual capacitance gives the total capacity of line 1.
The total capacitance is the sum of the capacitance to ground (eg, C1g for line 1) plus the mutual capacitances between the lines.
COUPLED WAVE EQUATIONS
- Wave Equation Revisited
- Coupled Wave Equations
Applying the isolated wire method to the current change caused by the capacitances of the coupled wire pays off. Note in equations (4-29) and (4-30) that the current change on line 1 caused by v1 is proportional to the sum of the capacitance to ground Cg and the mutual capacitance between the lines CM. In the second case, we assume that the same potential is applied to both lines.
In this situation, lines 1 and 2 remain at the same potential, so that no charge is stored in the electric field between the lines.
COUPLED LINE ANALYSIS
- Impedance and Velocity
- Coupled Noise
Cne=sum of the absolute values of the mutual capacitances of the lines that switch in phase with the line. The forward coupled wave then begins to propagate towards the far end of the victim line (z=l). The crosstalk noise propagates towards the near end of the victim's line where it is immediately detectable.
The shape of the close pulse depends on the electrical length of the coupled lines in relation to the transition time of the aggressor signal.
MODAL ANALYSIS
- Modal Decomposition
- Modal Impedance and Velocity
- Reconstructing the Signal
- Modal Analysis
Again, since the modal quantities are orthogonal, we can use them to simulate isolated system lines rather than coupled lines. Transmission line analysis requires us to determine the modal impedance and propagation velocity of the lines. The observable line voltage and currents that make up the signal propagating in the interconnect are linear combinations of modal values.
After decomposing the system into its orthogonal values and analyzing a set of n single lines corresponding to each mode to determine the modal voltages and currents, the observable line voltages and currents must be reconstructed using
Find, T v , the eigenvectors of LC
From inspection of the above equations, we note that Tv will satisfy the equation if Tv1= -Tv2, or Tv1=Tv2. While the matrices will be symmetric for a larger number of paired lines, the eigenvectors will change as a function of the values of the matrix entries. This gives us the information we need to construct the modal circuit for the odd mode, as shown in Figure 4-24.
Starting with the low-to-high transition at the voltage source, we use the equivalent odd-mode circuit in Figure 4.24 to calculate the voltage and current waves that are launched, assuming the rising edge occurs at time t=1 ns .
